I'm interested to know if there is a method for comparing the performance of two different models, such as a linear model and a linear mixed effect model on the same data set? I'm interested to compare these two statistical models and comment on their suitability for interpreting the data. Any suggestions would be greatly appreciated!
Test whether the random effects are significant using the likelihood ratio test. The parameters you're testing are on the boundary of the parameter space but the LRT is actually conservative in this case so you're good. If the random effects are not significant then use the regular linear model.